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Unformatted text preview: Week 5 ProfitMaximization Economic Profit • A firm uses inputs j = 1…,m to make products i = 1,…n. • Output levels are y. • Input levels are x 1 ,…,x m . • Product prices are p. • Input prices are w 1 ,…,w m. The Competitive Firm • Many firms. Each has no impact on prices. • The competitive firm takes all output prices p 1 ,…,p n and all input prices w 1 , …,w m as given constants. Economic Profit • The economic profit generated by the production plan (x 1 ,…,x m ;y) is • Firm’s problem is to maximize this economic profit. Π = . 1 1 m m x w x w py  = Π Economic Profit • Suppose the firm is in a shortrun circumstance in which • Its shortrun production function is y f x x = ( , ~ ). 1 2 x x 2 2 ≡ ~ . Economic Profit • Suppose in Short Run input 2 is fixed at some level Assume one output y. • Its production function is • The firm’s fixed cost is and its profit function is y f x x = ( , ~ ). 1 2 Π =   py w x w x 1 1 2 2 ~ . x x 2 2 ≡ ~ . FC w x = 2 2 ~ ShortRun IsoProfit Lines • An isoprofit line contains all the production plans that provide a particular profit level Π . • A Π isoprofit line’s equation is Π ≡   py w x w x 1 1 2 2 ~ . y w p x w x p = + + 1 1 2 2 Π ~ . ShortRun IsoProfit Lines y w p x w x p = + + 1 1 2 2 Π ~ has a slope of + w p 1 and a vertical intercept of Π + w x p 2 2 ~ . ShortRun IsoProfit Lines Π Π ≡ ′ Π Π ≡ ′′ Π Π ≡ ′′′ I n c r e a s i n g p r o f i t y x 1 Slopes w p = + 1 ShortRun ProfitMaximization • The firm’s problem is to locate the production plan that attains the highest possible isoprofit line, given the firm’s constraint on choices of production plans. • Q: What is this constraint? ShortRun ProfitMaximization • The firm’s problem is to locate the production plan that attains the highest possible isoprofit line, given the firm’s constraint on choices of production plans. • Q: What is this constraint? • A: The production function. ShortRun ProfitMaximization x 1 Technically inefficient plans y The shortrun production function and technology set for x x 2 2 ≡ ~ . y f x x = ( , ~ ) 1 2 ShortRun ProfitMaximization x 1 I n c r e a s i n g p r o f i t Slopes w p = + 1 y y f x x = ( , ~ ) 1 2 Π Π ≡ ′ Π Π ≡ ′′ Π Π ≡ ′′′ ShortRun ProfitMaximization x 1 y Π Π ≡ ′ Π Π ≡ ′′ Π Π ≡ ′′′ Slopes w p = + 1 x 1 * y * ShortRun ProfitMaximization x 1 y Slopes w p = + 1 Given p, w 1 and the shortrun profitmaximizing plan is Π Π ≡ ′′ x 1 * y * x x 2 2 ≡ ~ , ( , ~ , )....
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This note was uploaded on 01/07/2011 for the course ECON 2101 taught by Professor Fransis during the Spring '10 term at HKU.
 Spring '10
 fRANSIS

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